AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 156:565–576 (2015)

Angular Momentum and Arboreal Stability in Common Marmosets (Callithrix jacchus) Brad A. Chadwell1,2 and Jesse W. Young1,2,3* 1

Department of Anatomy and Neurobiology, Northeast Ohio Medical University (NEOMED), Rootstown, OH 44272 Skeletal Biology Research Focus Area, NEOMED, Rootstown, OH 44272 3 School of Biomedical Sciences, Kent State University, Kent, OH 44240 2

KEY WORDS evolution

balance; torque; center of mass; asymmetrical gaits; primate locomotor

ABSTRACT Despite the importance that concepts of arboreal stability have in theories of primate locomotor evolution, we currently lack measures of balance performance during primate locomotion. We provide the first quantitative data on locomotor stability in an arboreal primate, the common marmoset (Callithrix jacchus), predicting that primates should maximize arboreal stability by minimizing side-to-side angular momentum about the support (i.e., Lsup). If net Lsup becomes excessive, the animal will be unable to arrest its angular movement and will fall. Using a novel, highly integrative experimental procedure we directly measured whole-body Lsup in two adult marmosets moving along narrow (2.5 cm diameter) and broad (5 cm diameter) poles. Marmosets showed a strong preference for asymmetrical gaits (e.g., gallops and bounds) over symmetrical gaits (e.g., walks and runs), with asymmetrical gaits

representing >90% of all strides. Movement on the narrow support was associated with an increase in more “grounded” gaits (i.e., lacking an aerial phase) and a more even distribution of torque production between the fore- and hind limbs. These adjustments in gait dynamics significantly reduced net Lsup on the narrow support relative to the broad support. Despite their lack of a well-developed grasping apparatus, marmosets proved adept at producing muscular “grasping” torques about the support, particularly with the hind limbs. We contend that asymmetrical gaits permit small-bodied arboreal mammals, including primates, to expand “effective grasp” by gripping the substrate between left and right limbs of a girdle. This model of arboreal stability may hold important implications for understanding primate locomotor evolution. Am J Phys Anthropol 156:565–576, 2015. VC 2014 Wiley Periodicals, Inc.

The origins and subsequent diversification of primates are intimately linked to arboreality. Because the arboreal habitat is inherently discontinuous, multidimensional, and frequently unstable, primates face a host of locomotor challenges not encountered by more terrestrial mammals—a fact attested to by the frequency of long bone traumas due to falling in free-ranging arboreal primates (Lovell, 1991). As such, for nearly 100 years anthropologists have presented the need to move safely in an arboreal environment—specifically a narrowbranch arboreal environment—as one of the primary selective pressures shaping primate locomotor morphology and behavior (Wood Jones, 1916; Le Gros Clark, 1959; Napier, 1967; Cartmill, 1972; Larson, 1998). Despite the central role that concepts of arboreal stability have played in theories of primate locomotor evolution, we currently lack empirical measures of balance performance during primate locomotion. In this study, we provide the first quantitative in vivo data on locomotor stability in an arboreal primate, the common marmoset (Callithrix jacchus). In general, stability can be defined as the ability of a mechanical system to minimize the probability of catastrophic perturbations (Alexander, 2002; Full et al., 2002). We operationalize this concept by asserting that a primary index of arboreal stability is the control of the angular momentum of the center of mass (CoM) about the support (see also Lammers and Zurcher, 2011). Angular momentum has proved a useful metric of stability in a variety of systems, including insect hexapedalism, mammalian quadrupedalism, human bipedal walking, and robotics (Full et al., 2002; Goswami and Kallem, 2004; Herr and

Popovic, 2008; Lammers and Zurcher, 2011). We assume that primates seek to maximize arboreal stability by minimizing side-to-side rolling angular momentum about the support (abbreviated below as Lsup). If Lsup becomes too large, the animal will be unable to arrest its angular movement about the support and will fall (Cartmill, 1985; Preuschoft, 2002; Lammers and Zurcher, 2011). We describe a novel, highly integrative experimental protocol that integrates kinematic, kinetic, and gait data to directly measure Lsup during locomotion on narrow branch-like substrates. Our system expands on Lammers’ and colleagues research on torque production and arboreal stability in small, non-primate mammals (Lammers and Gauntner, 2008; Lammers and Zurcher,

Ó 2014 WILEY PERIODICALS, INC.

Additional Supporting Information may be found in the online version of this article. Grant sponsor: National Science Foundation; Grant number: BCS-1126790. *Correspondence to: Jesse W. Young, Department of Anatomy and Neurobiology, Northeast Ohio Medical University, 4209 State Route 44, P.O. Box 95, Rootstown, OH 44272. E-mail: jwyoung@neomed. edu Received 31 August 2014; revised 20 November 2014; accepted 24 November 2014 DOI: 10.1002/ajpa.22683 Published online 19 December 2014 in Wiley Online Library (wileyonlinelibrary.com).

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2011). We use our system to empirically test several long-held assumptions about the maintenance of stability during primate arboreal quadrupedalism. For example, traveling with a relatively flat and low trajectory of the CoM is thought to promote stability by reducing the moment arm of any potential toppling forces (Rose, 1973; Cartmill, 1985; Demes et al., 1990). Here, we test this hypothesis by directly quantifying the association between CoM height and Lsup. Additionally, because our system allows us to quantify torque production (i.e., twisting forces) from individual footfalls, we can address hypotheses of how primates modulate angular momentum control among and within limbs. We test four specific predictions: (P1) Provided that marmosets do not adjust locomotor behaviors to facilitate balance across different substrates, net change in Lsup over a stride (i.e., DLsup) will be greater on narrow supports, reflecting the challenge of maintaining stability as branch diameter decreases. Alternatively, similarity in average DLsup measures across substrates suggests an ability to increase stability via mechanical changes in locomotor behaviors. (P2) DLsup will be inversely proportional to the height of the CoM above the substrate, such that crouched postures are more stable. (P3) DLsup will be more closely associated with hind limb torque production than forelimb torque production, reflecting the primacy of the hind limb for maintaining arboreal stability (Cartmill, 1985; Szalay and Dagosto, 1988). (P4) Because marmosets lack a strongly developed grasping apparatus, torque will be generated primarily via the shearing action of substrate reaction forces acting about the radius of the support, rather than through the independent rotatory action of muscular grasping appendages (see also Lammers and Gauntner, 2008; Lammers, 2009a). We test these predictions by examining the gait dynamics of common marmosets moving over broad and narrow diameter supports (i.e., elevated poles). Although, through adaptation to gumnivory, marmosets have become quite derived relative to other primates (Sussman and Kinzey, 1984; Garber, 1992; Hamrick, 1998; Young, 2009; Smith and Smith, 2013), as smallbodied arboreal quadrupeds with claw-like tegulae on all digits except the hallux, marmosets, and other callitrichids have converged on the general morphotype thought to characterize the early stages of euprimate evolution (Szalay and Dagosto, 1988; Gebo, 2004; Bloch et al., 2007; Sargis et al., 2007). As such, empirical data on marmoset arboreal stability can serve as a baseline against which to evaluate balance performance in other, less-derived primates that adhere more closely to the crown primate bauplan (e.g., an animal with fully developed grasping extremities).

MATERIALS AND METHODS Experimental protocol Data were collected from two adult male common marmosets (Callithrix jacchus), housed at NEOMED. Before each experiment, marmosets were anesthetized with isoflurane and the lateral surfaces of the major forelimb joints (shoulder, elbow, wrist, and fifth metacarpalphalangeal joint), hind limb joints (hip, knee, ankle, and American Journal of Physical Anthropology

fifth metatarsal-phalangeal), and the base, tip, and midpoint of the tail were shaved and marked with retroreflective tape, to aid in later kinematic analysis. Following the marker placement, we recorded body mass to the nearest gram. Body mass for the two individuals averaged 370 g and 392 g, respectively. Upon recovery from anesthesia, the marmosets were encouraged with food rewards to cross a 4 m long set of horizontal poles at self-selected speeds (Fig. 1). Two pole diameters were used—a “narrow” 2.5 cm pole and a “broad” 5 cm pole. Six custom-built instrumented force poles were placed in series in the center of the pole trackway to record locomotor kinetics and two high-speed cameras (Xcitex XC-2; Xcitex, Woburn, MA) were located on either side of the animal to capture their movement patterns as they crossed over the force-sensitive region. Videos were recorded at 100–150 frames per second and the kinetic data channels were sampled at 60 scans per frame, resulting in scan rates of 6,000 or 9,000 Hz, respectively. Video and force data were synchronously recorded using the ProCapture system.

Data processing Only complete steady-state strides with minimal acceleration throughout the stride period were included in our dataset. Strides were considered complete when the animal’s body weight was entirely supported by the force poles during the stride (i.e., from touchdown to subsequent touchdown of a reference limb), ensuring complete mechanical measurement of all the substrate reaction forces (SRFs) and torques affecting the animal’s CoM movement. A stride was accepted as steady-state if the absolute forward acceleration across the stride was less than or equal to 5% of gravitational acceleration (i.e., 9.81 ms22). To track and quantify the three dimensional (3D) locomotor kinematics from both the left and right sides of the animals, we calibrated the temporally synchronized images from the four cameras to the same coordinate space using a three-step process (Standen and Lauder, 2005). More details on this process are provided in the online Supporting Information. In the final xyz-coordinate system, the xy-axes defined the horizontal plane with the x-axis parallel to the long axis of the pole substrate (i.e., the fore-aft [FA] direction) and the y-axis corresponding to the mediolateral (ML) direction. The zaxis defined the vertical (V) direction. The origin of the system was set to the midpoint of the force pole segments at their central axis (Fig. 1). For the strides meeting our selection criteria, joint markers on both sides of the body were digitized in ProAnalyst software (Xcitex, Woburn, MA). Each digitized feature was subsequently fit to a quintic smoothing spline function (tolerance of 1 mm2) using a custom MATLAB program, allowing us to mitigate digitizing error and interpolate the position of a feature for any frames where the marker was not visible (Walker, 1998). Force poles consisted of cylindrical wooden dowels attached to instrumented steel frames that were secured to a removable base. Each pole provided a measure of the substrate reaction forces (SRF) in the three axial directions (i.e., FA, ML, and V) and total torque (stot) about the support (based on the difference in vertical force registered on the left and right sides of the force pole). Force poles were calibrated by adapting the methods of Biewener and Full (1992) and Lammers and

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Fig. 1. Experimental system for recording the mechanics of simulated arboreal locomotion. (a) Schematic illustration of data recording apparatus. The 0.6 m long array of six strain gage force poles is set in the center of a series of raised horizontal poles, 4 m in total length. Lead wires from the strain gages are wired into Wheatstone bridge circuits, resulting in four channels for each force pole—one fore-aft (FA) channel, one mediolateral (ML) channel, and two vertical (V) channels from the left and right sides of the pole. The difference in force recorded by the two vertical channels provides a measure of rolling torque about the support (i.e., stot). A signal conditioning chassis excites the Wheatstone bridge circuits and also registers voltage changes in response to force pole loading. Three-dimensional kinematics are captured by two pairs of high-speed cameras, positioned on either side of the animal. A data collection computer synchronizes the video with the force data and stores bouts of data in response an external trigger press. (b) A captured video frame of a marmoset galloping through the experimental enclosure on the broad 5 cm substrate. (c) A close up of two force poles illustrating the two substrates used: a narrow 2.5 cm diameter pole and a broader 5 cm diameter pole.

Gautner (2008). More details on these procedures are provided in the online Supporting Information. All kinetic analyses were performed using a custom MATLAB program. Raw voltages from each force pole were first converted to Newtons (N) and corrected for cross talk between channels using the conversion factors obtained during the kinetic calibration process (see Supporting Information). A low-pass, fourth-order Butterworth filter was used to remove noise above 75 Hz for the FA and ML channels and 100 Hz for the two V channels.

Gait analyses For all strides in the dataset, the timing of the initial touchdown, the subsequent lift-off and the second touchdown for all four limbs were recorded. In cases where a limb was already in contact with a force pole at the start of the stride, the touchdown and lift-off of that stance phase were also noted. Additionally, we identified which force poles each foot contacted during its stance phase, allowing us to keep track of which limbs were associated

with the SRF recorded from each pole segment. Coding of the footfall timing and force pole identification was performed within ProAnalyst. Subsequent gait analyses were all performed in a custom-written MATLAB program. Temporal data on limb touchdown events were used for subsequent categorical gait coding. Strides in which the temporal lag between right and left forelimb stance periods, and between right and left hind limb stance periods, amounted to 50 6 10% of stride duration were categorized as symmetrical gaits. All other strides were categorized as asymmetrical gaits. Symmetrical gaits were further classified as lateral sequence or diagonal sequence gaits, and asymmetrical gaits as canters, gallops, bounds, or half-bounds, based on the temporal phasing of subsequent footfalls. Details of gait coding are provided in the online Supporting Information.

Primary outcome measures Angular momentum. Our primary metric of stability is the net change in angular momentum of the center of mass about the support (abbreviated as DLsup). Just as in linear American Journal of Physical Anthropology

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mechanics, where change in linear momentum is equal to the time integral of the applied force (i.e., impulse), the net change in angular momentum (i.e., angular impulse)Pcan P be calculated as the definite integral of stot, where stot is the sum of torques across all force poles over time, from the beginning to the end of the stride (t1 to t2): ð t2 X stot Dt: DLsup 5 t1

Angular momentum is quantified in units of N  cm  s. Note that because DLsup and angular impulse are synonymous terms, at times we refer to this quantity by either name, depending on the nature of the discussion. Center of mass height. calculated as:

CoM position was initially

mSh1ðmHp2mShÞ  pCoM; where mSh and mHp equal the midpoint between the left and right shoulders and hips, respectively, and pCoM is the average position of the CoM, as a percentage of trunk length from the shoulders to the hips. We estimated pCoM empirically for each animal using the reaction board method (Young, 2012). Details of this procedure can be found in online Supporting Information. Changes in CoM height during the stride were calculated via cumulative double integration of vertical CoM acceleration (where acceleration was calculated by subtracting body weight from the vertical SRF and dividing by body mass: Manter, 1938). Integrative constants were optimized using a path matching algorithm developed by Daley et al. (2006), as described in the online Supporting Information. Mean CoM height above the support surface over the stride was our primary metric of vertical posture during locomotion, with lower values indicating a “flatter” CoM trajectory. Interlimb and intralimb modulation of torque production. For those strides in which there was no temporal overlap between forelimbs and hind limbs on the same pole, we partitioned summed stot across the force poles into independent fore- or hind limb torque. We then calculated the portion of whole body DLsup due to the angular impulse developed by each girdle (i.e., DLsupFL and DLsupHL). In stance phases where isolated limbs contacted a given force pole segment, we could partition individual limb torques into two components (see Fig. 4 in Lammers, 2009b). First, torques can be produced as a result of the shearing components of vertical and mediolateral SRFs acting about the radius of the pole. We refer to this type of torque as substrate reaction torque (sSRF). Second, animals could use the rotatory action of the muscular grasping limbs to produce torques independent of those engendered by the SRF. We refer to this type of torque as muscular torque (smusc). Following Lammers and Gauntner (2008), we calculated sSRF and smusc as: sSRF 5rCoP 3SRFtr smusc 5stot 2sSRF ; where rCoP is the radial position of the limb’s center of pressure (CoP: the point location on the substrate surface through which the forces act) along the circumferAmerican Journal of Physical Anthropology

ence of the force pole, SRFtr is the substrate reaction force within the transverse plane (i.e., the V and ML components of the total SRF) and 3 indicates the cross product of the two vectors. We then evaluated the angular impulse of sSRF and smusc as metrics of the relative importance of the two mechanisms to the control of overall whole-body angular momentum. Standard force plates estimate the position of the CoP as the moment arm of any external torques applied to the plate. Such calculations assume that linear SRF are the only source of torques acting about the force transducer. Our force pole system clearly violates this assumption. We therefore kinematically estimated forelimb CoP as a point in the transverse midpoint of the palm, taken midway between the wrist and metacarpal-phalangeal joints. Because the feet were typically held in a digitigrade posture (as seen in most primates: Schmitt and Larson, 1995), we modeled hind limb CoP as the transverse midpoint across the metatarsal heads. During fast asymmetrical gaits, where two fore- or hind limbs contacted the same force pole as a functional unit, combined limb CoP position was estimated as the average of the individual limb CoP positions. In these cases, sSRF and smusc were calculated for the combined limb pair.

Statistical methods Categorical differences in gait selection according to substrate (e.g., symmetrical vs. asymmetrical gaits on broad and narrow substrates) were investigated using Fisher’s exact test of row-by-column independence (Sokal and Rohlf, 1995). Variation in continuous measures (e.g., DLsup) associated with gait type and substrate diameter was assessed using mixed-effects analyses of variance (ANOVA), analyses of covariance (ANCOVA), or regressions depending on the categorical or continuous nature of the predictor variables. The mixed-effects approach (Pinheiro and Bates, 2000), allowed us to appropriately adjust degrees of freedom and error terms to account for random variation among individuals and experimental days. The random factor for all models was experiment date nested within animal, guarding against pseudo-replication errors that could potentially arise by including multiple strides from the same animal for the same experiment date. Post hoc analyses were performed using Tukey’s HSD test (Sokal and Rohlf, 1995), modified for mixed-effects model structures. We used a model selection approach to evaluate the relative importance of various components of whole-body angular momentum control (i.e., forelimb torque vs. hind limb torque), calculating Akaike Information Criteria (AIC) for each model (i.e., predicting DLsup from forelimb torque alone vs. predicting DLsup from hind limb torque alone). The model with lowest rise in AIC relative to the full model (i.e., predicting DLsup from forelimb and hind limb torques together) indicated the best independent predictor of whole-body DLsup. Finally, we used paired t-tests to analyze the effects of a dichotomous predictor variable on a continuous paired measure (e.g., positive stot magnitudes vs. negative stot magnitudes within individual strides). All statistical analyses were performed using the R statistical platform (R Core Team, 2013).

RESULTS Our final dataset consisted of 63 strides, including 30 strides on the broad 5 cm diameter pole, and 33 strides

MECHANICS OF ARBOREAL STABILITY IN MARMOSETS a

TABLE 1. Frequency of gait use, grouped by substrate Asymmetrical HalfBound bound

Gallop

Symmetrical Canter

LS

DS

2.5 cm pole 1 (3%) 1 (3%) 4 (12%) 21 (64%) 3 (9%) 3 (9%) 5 cm pole – 2 (7%) 15 (50%) 13 (43%) – – a

Frequencies are expressed as absolute counts and, in parentheses, percentage of total strides within that substrate.

on the narrow 2.5 cm diameter pole. Marmosets used asymmetrical gaits much more frequently than symmetrical gaits (57 asymmetrical strides vs. 6 symmetrical). Of the 57 asymmetrical strides, most were either canters (34 strides) or gallops (19 strides). Half-bounds and full bounds were used infrequently (three strides and one stride, respectively). Asymmetrical gait selection differed significantly by substrate (P 5 0.01). Gallops and canters were used with relatively equal frequency on the broad support, whereas canters predominated on the narrow support (Table 1; Fig. 2). Symmetrical gaits were only used on the narrow 2.5 cm support, where they were split evenly between lateral sequence gaits (limb phases: 35–49%) and diagonal sequence gaits (limb phases: 51–62%; Table 1; Fig. 2). The mean limb phase for the symmetrical strides (695% confidence interval) was 46 6 5.2%, a value not significantly different from a trot (i.e., where limb phase equals 50% and contralateral fore- and hind limbs move in synchrony; t[5] 5 0.54, P 5 0.613). Given the distribution of sampled gaits in our dataset, and to create a more balanced design for distributional tests, we classified gaits into three categories for all subsequent analyses: symmetrical gaits, gallops/bounds (i.e., asymmetrical gaits with a whole-body aerial phase), and canters (i.e., asymmetrical gaits without a whole-body aerial phase). Marmosets used a range of speeds across symmetrical and asymmetrical gaits (symmetrical: 0.53–1.52 ms21; asymmetrical: 0.85–2.01 ms21). Mixed-effects ANOVA revealed a significant main effect for gait type (Fig. 3; F[2,52] 5 3.4, P 5 0.041) but not for substrate diameter (F[1,6] 5 0.78, P 5 0.411). Speed tended to be greatest during galloping/bounding gaits, though the individual post hoc comparisons did not reach a a  0.05 level of significance (P 5 0.053 and 0.096 for comparisons of gallops/ bounds with symmetrical strides and canters, respectively).

Angular momentum Total substrate reaction torque (stot) typically fluctuated about zero during a stride (Fig. 4, also see Movies S1-S3 in the online Supporting Information). On average, stot changed direction 4.5 times during a stride (range: 0–10 times). The magnitudes of the net positive and negative changes in angular momentum (DLsup) induced by these fluctuations in stot were not statistically different from one another on the narrow substrate (paired t-test: t[32] 5 0.628, P 5 0.535), but were so on broad substrate (paired t-test: t[28] 5 22.45, P 5 0.021). These data suggest that the marmosets exerted more balanced rolling torques when moving on the narrow substrate, perhaps as a means of reducing overall fluctuations in Lsup. Indeed, the net change in angular momentum (DLsup) over a stride was significantly lower

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on the narrow substrate (Fig. 5; F[1,6] 5 9.2, P 5 0.023). On the narrow diameter pole, DLsup was significantly associated with gait type (F[2,25] 5 5.5, P 5 0.010), such that DLsup was higher when marmosets used gallops/ bounds than when they used canters or symmetrical gaits (P  0.011). Gait type was not significantly associated with variation in DLsup on the broad diameter pole (F[1,24] 5 0.32, P 5 0.577).

Effects of CoM height Average CoM height over a stride was significantly associated with gait type (F[2,52] 5 3.47, P < 0.039), but not substrate diameter (F[1,6] 5 1.31, P 5 0.297) (Fig. 6). CoM height was greater during galloping and bounding gaits than during canters or symmetrical gaits (P 5 0.028 and 0.011, respectively). Contrary to our predictions, DLsup was not directly associated with variation in CoM height either across substrates (Fig. 7; F[1,53] 5 0.01, P 5 0.918) or independently within each substrate (all P  0.848).

Hind limb versus forelimb regulation of whole-body angular momentum On the broad substrate, the net change in angular momentum (DLsup) associated with hind limb angular impulse (i.e., DLsupHL) was significantly greater than that associated with forelimb angular impulse (i.e., DLsupFL) (P 5 0.002), whereas on the narrow substrate DLsupFL and DLsupHL magnitudes were statistically similar (P 5 0.677) (Fig. 8). Mixed-effects regression, fit separately for each pole diameter, revealed that on the broader substrate DLsup was more closely associated with DLsupHL than with DLsupFL (DLsupFL R2: 0.80; DLsupHL R2: 0.93). A model predicting DLsup from DLsupHL alone also resulted in the lowest rise in AIC relative to a full model that included both DLsupHL than DLsupFL (DLsupFL model AIC: 8.9; DLsupHL model AIC: 222.8; full model AIC: 2196.3). In contrast, on the narrow substrate, DLsup was slightly better predicted by DLsupFL than DLsupHL (DLsupFL R2: 0.85; DLsupHL R2: 0.82), and a model including DLsupFL also resulted in the lowest rise in AIC relative to the full model (DLsupFL model AIC: 26.7; DLsupHL model AIC: 22.3; full model AIC: 2151.7) (Fig. 8). In sum, on the broad substrate, whole-body angular momentum was most directly determined by hind limb torque production. On the narrow substrate, the two limbs shared a more equal division of labor, though changes in whole-body angular momentum were slightly more closely associated with forelimb torque production. There were no significant interactions with gait type (all P  0.105), indicating that interlimb differences in angular momentum control were similar across gaits.

Mechanism of torque production: sSRF versus smusc We quantified the relative importance of sSRF versus smusc by measuring the angular impulse imparted by each mechanism of torque production. A mixed-effects ANOVA revealed a significant interaction between source (i.e., smusc or sSRF) and limb girdle (F[1,137] 5 10.7, P 5 0.001), such that whereas smusc angular impulse was greater than sSRF angular impulse across limb girdles (all P < 0.001), the differentiation between smusc and sSRF angular impulse was most pronounced in the hind limbs American Journal of Physical Anthropology

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Fig. 2. Variation in gait selection as a function of substrate diameter. The frequencies of each gait type are expressed as percentages of the total number of strides collected on the indicated substrate diameter.

the pole than the hind limbs (Figs. 10 and 11; all P < 0.001). Within the hind limbs, more laterally placed CoP positions were significantly associated with lower sSRF angular impulse (Spearman’s non-parametric correlation: q 5 20.42, P 5 0.002), suggesting that limb placement may have at least partially accounted for the greater differentiation between smusc and sSRF angular impulse in the hind limbs than in the fore limbs.

DISCUSSION

Fig. 3. Interaction plot of average speed differences between substrate diameters, grouped by gait type. Error bars indicate 95% confidence intervals about the mean for each cell.

(Fig. 9). Specifically, whereas sSRF angular impulses were statistically similar between the limb girdles (P 5 0.537), smusc angular impulses were significantly greater in the hind limbs than in the forelimbs (P 5 0.001). Because the position of the CoP along the circumference of the pole is a primary determinant of the effectiveness within which animals can exert sSRF or smusc (Lammers and Gauntner, 2008), we also investigated variation in average forelimb and hind limb CoP position across substrate diameters. For these analyses, we quantified CoP location as angular position relative to the top of the force pole, such that 0 would represent placement directly on top of the pole and 90 would represent placement on the lateral extreme of the pole. A mixedmodel ANOVA, including substrate diameter and limb girdle as factors, revealed significant main effects for both diameter (F[1,6] 5 29.9, P 5 0.002) and limb girdle (F[1,61] 5 76.8, P < 0.001), and no interaction between the two (F[1,61] 5 0.06, P 5 0.806). Irrespective of limb girdle, marmosets positioned the extremities closer to the top of pole when moving on the broad substrate than when moving on the narrow substrate (Figs. 10 and 11; all P < 0.001). Similarly, irrespective of substrate diameter, marmosets positioned the forelimbs closer to the top of American Journal of Physical Anthropology

The marmosets in our sample proved adept at limiting fluctuations in angular momentum and maintaining arboreal stability, though not all our specific predictions regarding angular momentum control were supported. Additionally, it should be noted that DLsup values were significantly greater than zero across the dataset (Fig. 5), suggesting that rolling plane stability is likely maintained by managing net angular momentum across strides, rather than within strides. As Lammers and Zucher (2011) note, the observation that stability is likely maintained across strides call into question the common practice of using the stride as the unit of analysis in locomotor studies, suggesting instead that broad control strategies may only be apparent in mechanical data collected across bouts of strides. However, such ambitious protocols are difficult in animal research, where measuring extended bouts of locomotor typically requires the use of a treadmill, with potentially biasing effects (Blaszczyk and Loeb, 1993). The range of rolling plane angular impulses documented for marmosets—adjusted for body size by dividing DLsup by the product of body mass, average CoM height, and gravitational acceleration—are broadly similar to values previously reported for chipmunks (Tamias sibiricus) running on a simulated arboreal trackway, the only other quadrupedal mammal for which similar data are available (marmosets: 20.043 to 0.022 vs. chipmunks: 20.026 to 0.023; chipmunk data from Lammers and Zurcher, 2011). However, peak size-adjusted Lsup in the marmosets was nearly three times larger than comparable values reported for walking humans (Herr and Popovic, 2008)—though it is perhaps not surprising that

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Fig. 4. Gait mechanics of an exemplar stride (a canter on the narrow 2.5 cm pole; see Supporting Information Movie S2). (a) The gait graph of the stride, where bars indicate the stance phase period of each limb. (b–d) Fore-aft (FA), mediolateral (ML), and vertical (V) substrate reaction forces during the stride. (e, f) Total torque (stot) across the force poles and whole-body angular momentum about the support (Lsup). Throughout the top four panels, different colors and line styles correspond to footfalls on different force poles. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

large, slow moving bipeds would seek to limit side-toside angular momentum more so than small-bodied, agile arboreal quadrupeds. We predicted that marmosets would show greater instability on the narrow substrate, reflecting the challenge of maintaining balance as branch diameter decreases. However, DLsup was actually greatest on the broad substrate (Fig. 5), suggesting greater instability on the larger diameter support. Two possible explanations could account for this phenomenon. First, it may be that marmosets could tolerate increased DLsup on the 5 cm support because the greater size of the substrate

made it easier to correct balance perturbations. Analysis of average fore- and hind limb CoP positions showed the larger diameter of the 5 cm pole allowed marmosets to maintain contact points closer to the top of the support (Figs. 10 and 11), making the broad support functionally more similar to terrestrial locomotion (Jenkins, 1974). By maintaining limb contacts closer to the top of the pole, vertically oriented forces—which are by far the largest component of the total resultant force exerted on substrate (Fig. 4)—would primarily act perpendicular to pole’s surface, allowing the animal to more easily correct balance disturbances via the application of normal American Journal of Physical Anthropology

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Fig. 5. Interaction plot of average differences in DLsup between substrate diameters, grouped by gait type. Error bars indicate 95% confidence intervals about the mean.

Fig. 6. Interaction plot of average differences in CoM height between substrate diameters, grouped by gait type. Error bars indicate 95% confidence intervals about the mean.

(rather than shearing) forces. Moreover, due to the larger radius of the support, the animal would have to generate proportionally less shearing force to counter any disruptive torques about the support. In sum, it could be that on the broader support marmosets tolerated greater DLsup within strides because counteracting any excessive angular momentum during the next stride would be comparatively easier. Alternatively, it could be that reduced DLsup on the 2.5 cm pole indicates that the marmosets successfully adjusted their gait mechanics to mitigate the stability challenges that might have occurred on the narrow support. Marmosets significantly altered gait selection when moving on the narrow support, eschewing gallops and bounds in favor of symmetrical gaits and canters (Table 1, Fig. 2). Young (2009) documented a similar shift away from aerial phase gaits to more grounded asymmetrical gaits as marmosets and squirrel monkeys transitioned from locomotion on a flat runway to locomotion on a raised pole. The use of more grounded gaits, such as canters, is thought to reduce both CoM displacements and the magnitude of peak forces imparted to the substrate (Schmitt et al., 2006; Young, 2009). Indeed, in the current dataset, both CoM heights and peak vertical forces were greater during galloping/bounding gaits than

during canters or symmetrical gaits (Fig. 6; all P  0.028). In an arboreal context, such changes could reduce branch oscillations and thus promote stability (Demes et al., 1990). Additionally, the use of canters and symmetrical gaits was associated with significantly reduced DLsup when marmosets were moving on the narrow support, suggesting that “grounded” gaits can increase lateral stability as well (Fig. 5). Finally, narrow branch locomotion was associated with a more equal division of whole-body DLsup control between the forelimbs and the hind limbs (Fig. 8). Though this partially contradicts our prediction that the hind limbs would consistently play a greater role in controlling whole-body angular momentum, it may be that the equal division of labor on the narrow support permitted more subtle control over DLsup throughout the stride. Indeed, fluctuations in stot were more balanced between positive and negative torques on the narrow substrate. Increasing joint flexion and moving with a crouched posture have long been argued to be a primary behavioral means of increasing arboreal stability (Napier, 1967; Rose, 1973; Schmitt, 2003b; Schmidt and Fischer, 2010). Crouched postures are argued to promote stability by bringing the CoM closer to the substrate, thus limiting the magnitude of any potential toppling torques by

Fig. 7. Association between net change in angular momentum (DLsup) and CoM height on the narrow (a) and broad (b) diameter poles, grouped by gait type.

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shortening their moment arms. We tested this hypothesis by examining the correlation between CoM height and DLsup. Though we found no evidence for a direct correlation between these variables, it is noteworthy that the variance of DLsup tended to increase in proportion to CoM height (Fig. 7). As such, the highest values of DLsup were observed when the CoM was furthest from the substrate, though the inverse was not true (i.e., that low values of DLsup were only observed when the CoM was closest to the substrate). Functionally, this suggests that although high CoM positions may have been associated with increased DLsup, marmosets were able to use other mechanisms to limit the destabilizing effects of this relationship. For instance, studies of dynamic stability during human walking have found that lateral stability increases with speed (Bruijn et al., 2009). Because CoM height was greatest when marmosets used the fastest gaits (Fig. 6), it may be that the increased dynamic stability conferred by high speeds at times mitigated the instability that might have resulted from high CoM positions. Future studies of slower moving arboreal animals may find a more direct correlation between CoM height and DLsup. Long, mobile digits adapted for grasping are often cited as a key morphological trait defining the Order Primates (Le Gros Clark, 1959; Dagosto, 2007). Functionally, grasping extremities are thought to facilitate adhesion and balance on narrow substrates by allowing

primates to generate stabilizing muscular torques about the support (Napier, 1967; Cartmill, 1985; Preuschoft et al., 1995). Through adaptation to gumnivory, marmoset autopodial anatomy has become quite derived relative to other crown primates, being characterized by claw-like tegulae on every digit but the hallux, relatively narrow apical pads, and a relatively short hallux with diminished adductor musculature (Beattie, 1927; Midlo, 1934; Hamrick, 1998). These derived changes in marmoset autopodial morphology may limit grasping ability when locomoting in a small branch environment (Hamrick, 1998; Schmitt, 2003a). We thus predicted that limited grasping morphology would require marmosets to produce angular impulse primarily through substrate reaction forces (i.e., sSRF) rather than the independent rotatory action of muscular grasping limbs (i.e., smusc). In contradiction to this prediction, across limb girdles and substrate diameters, angular impulse was predominantly generated via smusc, with the discrepancy between smusc and sSRF being particularly pronounced in the hind limbs (Fig. 9). Despite their limited development of typical primate grasping morphology, marmosets were thus nonetheless able to control lateral stability via primarily muscular torque production. We contend that the discrepancy between our prediction and our findings results from the marmosets’ predominant use of asymmetrical gaits. Most hypotheses of primate locomotor evolution typically assume (either implicitly or explicitly) that early primates and their ancestors were using symmetrical gaits, where footfalls would be spaced in time and each limb would function more or less independently (e.g., Cartmill, 1972; Szalay and Dagosto, 1988; Sussman, 1991; Larson, 1998). In such a situation, individual extremities would be responsible for producing the torques required to regulate whole-body angular momentum, making grasping morphologies beneficial. During asymmetrical gaits, however, the two limbs of a girdle function together, producing substrate reaction forces and torques as a single unit. As such, the forelimbs and hind limbs of a cantering, galloping, or bounding primate could be considered to represent unified “functional extremities,” expanding “effective” grasp as the animal grips the substrate between the left and right limbs of the girdle. Moreover, because hind limbs typically have shorter lead durations than forelimbs during asymmetrical gaits, particularly among small mammals (Dagg, 1973; Hildebrand, 1977), the tendency for

Fig. 9. Interaction plot of the average differences in DLsup accounted for by smusc versus sSRF in forelimbs and hind limb. Error bars indicate 95% confidence intervals about the mean.

Fig. 10. Interaction plot of average differences in angular CoP position between substrate diameters, grouped by limb girdle. Error bars indicate 95% confidence intervals about the mean.

Fig. 8. Interaction plot of average differences in forelimb and hind limb angular impulse (i.e., DLsup) grouped by substrate diameter. Error bars indicate 95% confidence intervals about the mean.

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Fig. 11. Anterior view of mean CoP positions for right limbs (dark-shaded symbols) and left limbs (light-shaded symbols), grouped by substrate diameter and gait type. Radial lines on each pole are spaced at 30 intervals. Symbols are plotted at different levels along the circumference of the pole to more easily distinguish among gait types. All calculations involving CoP position assumed a location on the surface of the pole.

the two limbs in a girdle to function as a single extremity is likely to be most pronounced in the hind limbs. In the current dataset, average hind limb lead durations (scaled to trailing limb duty factors, following Hildebrand, 1977) were approximately half of average forelimb lead durations (forelimbs: 52.2%; hind limbs: 26.2%), a difference that was significant on both substrates (all P  0.001). Additionally, the relatively low position of the hind limbs on the pole (Figs. 10 and 11) could have permitted the animals to more effectively grip the substrate between the right and left feet by exerting opposing normal forces, further facilitating smusc production (Cartmill, 1974). The use of paired left and right limbs as unified grasping organs may also explain the frequent use of trot-like symmetrical gaits in marmosets and other callitrichids (Arms et al., 2002; Schmitt, 2003a; Nyakatura et al., 2008; Nyakatura and Heymann, 2010; this study), as well as during arboreal locomotion in other small non-grasping mammals, such as opossums (Lammers and Gauntner, 2008). In a trotting gait, left and right fore- and hind limbs are paired across limb girdles, in this case permitting contralateral forelimb-hind limb pairs to act as unified “functional extremities.” Indeed, Lammers and Gauntner (2008) showed that average smusc exceeded average sSRF in trotting gray short-tailed opossums (Monodelphis domestica) moving over instrumented poles, supporting our contenAmerican Journal of Physical Anthropology

tion that paired limb use permits non-grasping mammal to effectively control torque production about the substrate. In summary, the use of asymmetrical gaits allowed marmosets to create functional grasping appendages, facilitating the production of muscular torques about the substrate despite their relatively poor development of typical primate grasping morphology. This hypothesized relationship between asymmetrical gaits and the creation of functional grasping appendages may explain the frequent use of asymmetrical gaits in other small-bodied arboreal mammals, including didelphid marsupials (Pridmore, 1994), tree squirrels (Youlatos and Samaras, 2010), tree shrews (Jenkins, 1974), mouse lemurs (Shapiro et al., 2014), and other callitrichids (Fleagle and Mittermeier, 1980; Garber, 1991; Rosenberger and Stafford, 1994; Nyakatura and Heymann, 2010). As noted above, high speed asymmetrical gaits also confer dynamic stability, further mitigating arboreal balance disruptions (Bruijn et al., 2009). Moreover, postcranial features of Eocene primates and other closely related archontan taxa suggest that asymmetrical gaits may have been a critical component of the locomotor repertoire of stem primates and their ancestors (Gregory, 1920; Dagosto, 1993, 2007; Bloch and Boyer, 2007), particularly during those stages of primate evolution when overall body sizes were small and a powerful pedal

MECHANICS OF ARBOREAL STABILITY IN MARMOSETS grasping apparatus had yet to be developed (Gebo, 2004; Sargis et al., 2007). However, because substrate reaction forces are typically greater during high-speed locomotion, an inevitable trade-off is reached as overall body size increases relative to branch diameter. At some point, either branch integrity would be compromised or angular momentum in other planes would become excessive (e.g., pitching momentum in the sagittal plane), and the use of asymmetrical gaits would be detrimental to arboreal stability. In these situations, grasping extremities should confer some selective performance advantage. Because branches are not vanishingly small, small-bodied arboreal mammals are less likely to encounter such challenging substrates on a frequent basis. We acknowledge that grasping extremities can serve functions beyond the maintenance of balance during horizontal arboreal locomotion, and are also likely to be critical for climbing and the traversal of oblique supports (Reghem et al., 2012; Birn-Jeffery and Higham, 2014). Nevertheless, we suggest that in general there may have therefore been a “body size threshold” during primate locomotor evolution, past which powerful grasping extremities and behavioral adjustments—such as the use of compliant gait kinematics (Schmitt, 1999, 2003b) and specific footfall patterns, such as diagonal sequence gaits (Stevens, 2006, 2007)—became critical adaptations for maintaining arboreal stability, facilitating early primates’ successful restriction to the arboreal habitat (Orkin and Pontzer, 2011).

CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH The primary goal of this study was to introduce a novel conceptual and experimental framework with which to evaluate stability during primate quadrupedal locomotion. As illustrated by our case study of common marmosets, this system has the potential to provide new empirical insight into the performance benefits of morphological and behavioral features that have long been argued to be critical elements of primate quadrupedalism. Ongoing research in our laboratory is using this framework to examine locomotor stability in other primates for whom symmetrical gaits are more common (e.g., squirrel monkeys, Saimiri boliviensis). To better model the complexity of wild primate locomotion, future studies should also consider how intermittent locomotion (vs. the continuous steady-state strides studied here) and greater substrate variability impact the quantitative metrics of primate stability introduced here. Such data are required to fully explore the links among morphology (broadly defined here to include both locomotor anatomy and behavior), function (the production of forces and torques), and performance (the maintenance of arboreal stability). Organizing research questions along this morphology–function–performance axis is a crucial step in establishing the adaptive nature of a given feature (Arnold, 1983; Lauder, 1996), and is thus critical to understanding primate locomotor evolution.

ACKNOWLEDGMENTS The authors thank Nathan Michael, Timothy O’Neill, Kyle Resnick, and Gabrielle Russo for help with animal experiments and data processing. Nicolay Hristov provided invaluable advice on animal training. The NEOMED Comparative Biomechanics Journal Club, the associate

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editor, and the two external reviewers provided helpful comments on a previous draft of this manuscript. Research supported by NSF-BCS 1126790 and the NEOMED Department of Anatomy and Neurobiology.

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